ATLANTA—In the small Georgia town of Demorest, Habersham Medical Center, like many rural hospitals, has seen its patient base change in a way that hurts its bottom line. As unemployment in the northeast Georgia mountains remains stubbornly high, more of the hospital's patients have no health insurance. Among those patients with private coverage, an increasing number have high-deductible policies, which means that patients must pay all or a large portion of the bills out of pocket. And a large share of patients have Medicaid, the federal-state program for low-income people that often doesn't reimburse enough to cover the cost of services, hospital officials say.